A Proof of a Conjecture of Marino-Vafa on Hodge Integrals

By Chiu-Chu Melissa Liu, Kefeng Liu, Jian Zhou. 2003

164 citations recorded by the source corpus.

We prove a remarkable formula for Hodge integrals conjectured by Marino and Vafa based on large N duality, using functorial virtual localization on certain moduli spaces of relative stable morphisms.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c55644f8f04f2a4c6af5374e284449475d9188fb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

1. Marcos Mariño
2. R. Pandharipande
3. A. Okounkov
4. B. Eynard
5. M. Mulase
6. Ravi Vakil
7. Davesh Maulik
8. N. Orantin

In Geometry and Topology

1. Marcos Mariño
2. R. Pandharipande
3. A. Okounkov
4. C. Vafa
5. B. Eynard
6. A. Klemm
7. Mina Aganagic
8. Davesh Maulik

In Mathematical Physics

1. Marcos Mariño
2. R. Pandharipande
3. B. Eynard
4. C. Vafa
5. A. Okounkov
6. Mina Aganagic
7. A. Klemm
8. N. Orantin

Citations in the corpus

• Gromov-Witten/Donaldson-Thomas correspondence for toric 3-folds (2008, background): “The 1-leg version of the topological vertex appeared first in [21] and was proven in [19, 28].”
• Polynomial recursion formula for linear Hodge integrals (2009, background): “The other parameter s counts the number r of simple ramification points.”
• THE MODULI SPACE OF CURVES AND GROMOV-WITTEN THEORY (2006, methodology): “ of the moduli space. It would be very interesting, and potentially important, to remove hypotheses (1) and (2). The theory of virtual localization can be applied to our relative setting [GrV3]. (See [LLZ] for more discussion.) Wenow describe it in the case of interest to us, of maps to P1. Again, i”
• The Laplace transform of the cut-and-join equation and the Bouchard-Marino conjecture on Hurwitz numbers (2009, methodology): “It has become an effective tool for studying algebraic geometry of Hurwitz numbers and many related subjects [4, 18, 19, 20, 25, 26, 28, 30, 41, 45].”
• Topological Strings and Integrable Hierarchies (2003, background): “Notice that this operator, when written as a differential operator on coherent wave state functions, is the “cut and join” operator considered for example in [19].”
• Computation of Open Gromov–Witten Invariants for Toric Calabi–Yau 3-Folds by Topological Recursion, a Proof of the BKMP Conjecture (2012, methodology): “For our purpose here, we shall start directly from the localization formula of [42], and which is the straightforward generalization of theorem 3.”
• A mathematical theory of the topological vertex (2004, background): “The main result of [30] is the following formula conjectured by Mariño and Vafa [33] (see [40] for another proof): Theorem 8.”
• Hodge integrals and invariants of the unknot (2003, methodology): “(2.1) We will transform the above formula by commuting the operators Γ+(iu) and eauF2 , which fix the vacuum vector, through the operators α−µi .”
• Chern-Simons theory and topological strings (2004, unknown): “This idea has been difficult to implement, but in recent years some spectacular progress was made thanks to the work of Maldacena (1998), who postulated a duality between type IIB string theory on AdS5 × S(5) and N = 4 super Yang-Mills with gauge group U(N).”